This paper investigates the system-level throughput of non-orthogonal multiple access (NOMA) with a successive interference canceller (SIC) in the cellular downlink assuming proportional fair (PF)-based radio resource (bandwidth and transmission power) allocation. The purpose of this study is to examine the possibility of applying NOMA with a SIC to the systems beyond the 4G cellular system. Both the mean and cell-edge user throughput are important in a real system. PF-based scheduling is known to achieve a good tradeoff between them by maximizing the product of the user throughput among users within a cell. In NOMA with a SIC, the scheduler allocates the same frequency to multiple users simultaneously, which necessitates multiuser scheduling. To achieve a better tradeoff between the mean and cell-edge user throughput, we propose and compare three power allocation strategies among users, which are jointly implemented with multiuser scheduling. Extensive simulation results show that NOMA with a SIC with a moderate number of non-orthogonally multiplexed users significantly enhances the system-level throughput performance compared to orthogonal multiple access (OMA), which is widely used in 3.9 and 4G mobile communication systems.